Voilum-1: An Execution-Grounded Mixture-of-Experts SLM for Computational Python & Machine Learning Systems

Elise Paul
Independent AI Research & Systems
Hugging Face Profile • Model Repository

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Abstract

We introduce Voilum-1, a high-efficiency 463.6-million parameter (100.8M active parameters per token) sparse Mixture-of-Experts (MoE) Small Language Model (SLM) specialized for deterministic, mathematically rigorous Python code synthesis, numerical scientific computing, and deep learning systems implementation. Trained across 12.0 billion tokens of curated algorithmic and mathematical data, aligned via ChatML instruction tuning, and reinforced through a 6-tier curriculum of execution-grounded Group Relative Policy Optimization (GRPO), Voilum-1 solves complex machine learning tasks from conceptual specifications without code spoon-feeding. In empirical sliding-window evaluations, Voilum-1 achieves a 99.3% greedy pass rate on challenging applied machine learning and numerical systems benchmarks while operating within an ultra-compact memory footprint of 884 MB in BF16 SafeTensors.

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1. Architectural Specifications

Voilum-1 employs a decoder-only sparse Mixture-of-Experts architecture incorporating Grouped-Query Attention (GQA), Rotary Position Embeddings (RoPE), RMSNorm, and SwiGLU gating:

Architectural Hyperparameter	Specification	Description
Total Parameters	463,553,024 (463.6M)	Full weights memory footprint (884 MB in BF16)
Active Parameters / Token	100,800,000 (~100.8M)	Parameters engaged in each forward pass
Transformer Layers ( (N_{\text{layers}}) )	16	Pre-norm decoder blocks
Hidden Dimension ( (d_{\text{model}}) )	512	Model channel representation dimension
Feed-Forward Routing	8 Experts (Top-1 / Top-2)	Sparse token-level gating with softmax load balancing
Expert Intermediate Dim	2,048	SwiGLU projection dimension per expert
Attention Mechanism	Grouped-Query Attention (GQA)	8 Query heads, 2 Key-Value heads (4:1 compression)
Head Dimension ( (d_k) )	64	Per-head projection dimension
Positional Encoding	Rotary Embeddings (RoPE)	Base frequency ( \theta = 10,000.0 )
Normalization	RMSNorm	Zero-mean centering omitted for scale invariance: ( \epsilon = 10^{-6} )
Activation Function	SwiGLU	Gated Swish-linear non-linearity
Context Length ( (L_{\text{ctx}}) )	2,048 tokens	Native autoregressive training horizon
Vocabulary Size ( (V) )	49,152	Byte-Pair Encoding (StarCoder2 BPE)

Layer Dataflow & Computation

Each decoder layer executes the following standardized pre-norm transformation sequence:

1. Pre-Attention Normalization: Input representation ( x ) is normalized via Root Mean Square Normalization:

$$\text{RMSNorm}(x,ϵ={10}^{-6})=\frac{x}{\sqrt{\frac{1}{d}\sum _{i=1}^d{x}_i^2+ϵ}}\odot \gamma \backslash text\{RMSNorm\}(x,\; \backslash epsilon=10^\{-6\})\; =\; \backslash frac\{x\}\{\backslash sqrt\{\backslash frac\{1\}\{d\}\backslash sum\_\{i=1\}^\{d\}\; x\_i^2\; +\; \backslash epsilon\}\}\; \backslash odot\; \backslash gamma$$

2. Grouped-Query Attention (GQA): 8 query heads interact with 2 shared key-value heads (4:1 KV compression), rotated with RoPE position embeddings (base ( \theta=10,000.0 )). The resulting attention context is added to ( x ) via residual connection:

$$\text{Attention}(Q,K,V)=\text{softmax}\left(\frac{Q{K}^T}{\sqrt{d_k}}\right)V\backslash text\{Attention\}(Q,\; K,\; V)\; =\; \backslash text\{softmax\}\backslash left(\backslash frac\{Q\; K^T\}\{\backslash sqrt\{d\_k\}\}\backslash right)\; V$$

3. Pre-FFN Normalization: The attention output is normalized through a second RMSNorm layer.

4. Sparse Mixture-of-Experts Feed-Forward: A learnable routing gate computes softmax probabilities over 8 experts. The top-2 activated experts evaluate independent SwiGLU transformations with intermediate projection dimension 2,048:

$$\text{SwiGLU}(x)=(\text{Swish}(x{W}_{\text{gate}})\otimes (x{W}_{\text{up}}))W_{\text{down}}\backslash text\{SwiGLU\}(x)\; =\; \backslash left(\backslash text\{Swish\}(x\; W\_\{\backslash text\{gate\}\})\; \backslash otimes\; (x\; W\_\{\backslash text\{up\}\})\backslash right)\; W\_\{\backslash text\{down\}\}$$

The routed expert outputs are dynamically weighted by routing probabilities, summed, and added to the residual stream.

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2. Training Methodology & Curriculum Progression

Voilum-1 was developed through a three-stage progressive optimization pipeline:

• Stage 1: Base Pretraining (12.0 Billion Non-Repeating Tokens)
  Pretrained on a highly curated corpus spanning scientific Python (NumPy, SciPy, Pandas), PyTorch deep learning internals, algorithms, and numerical mathematics. Optimized with AdamW (peak learning rate ( 5 \times 10^{-4} ), linear warmup, cosine decay, bfloat16 mixed precision).

• Stage 2: Direct Instruction SFT Alignment
  Aligned using ChatML formatting (<|im_start|> / <|im_end|>) under a strict Zero-Thinking Token policy. The model is trained to produce clean, direct, executable code without conversational boilerplate or unstructured internal monologue.

• Stage 3: Pedagogical T-GRPO Reinforcement Learning (Tiers 1 to 6)
  Post-trained using Group Relative Policy Optimization (GRPO) with signed advantage baselines (( G = 4 ) rollouts per prompt) and KL penalty against the Stage 2 reference policy. Evaluated via an automated, isolated compiler and unit-test execution sandbox across 6 pedagogical mastery tiers.

2.1 The Zero-Code Authentic Problem Solving Standard (Tier 6)

Unlike conventional coding benchmarks that spoon-feed mathematical equations directly inside the prompt (e.g. rms = torch.sqrt(torch.mean(x**2) + eps)), Voilum-1 is reinforced against authentic engineering and applied system specifications:

• The Problem Framing: Outlines the theoretical motivation, invariant properties, and mathematical constraints.
• The Interface Specification: Defines expected function/class signatures, input/output tensor ranks, and data types.
• Zero Implementation Dictation: The model autonomously formulates algorithmic transformations, dimensional broadcasting, and vectorized execution from first principles.

2.2 Curriculum Benchmarks Across All 6 Mastery Tiers

All tiers were evaluated under strict deterministic greedy decoding (( T = 0.0, \text{argmax} )) over rolling evaluation windows of ( W = 15 ) (300 training steps):

$$\text{Rolling Greedy Pass Rate}=\frac{1}{W}\sum _{k=1}^W{\text{GreedyEval}}_k\ge 25.0\mathrm{\%}⟹\text{Tier Mastered}\backslash text\{Rolling\; Greedy\; Pass\; Rate\}\; =\; \backslash frac\{1\}\{W\}\; \backslash sum\_\{k=1\}^\{W\}\; \backslash text\{GreedyEval\}\_k\; \backslash ge\; 25.0\backslash \%\; \backslash implies\; \backslash text\{Tier\; Mastered\}$$

Curriculum Tier	Domain & Problem Scope	Problem Pool	Mastery Threshold	Final Greedy Pass Rate	Evaluation Result
Tier 1	Python Language Primitives & Foundations	600	25.0%	85.0%	MASTERED
Tier 2	Probability Theory & Statistical Formulations	328	25.0%	25.3%	MASTERED
Tier 3	Calculus, Linear Algebra & Core Algorithms	2,400	25.0%	94.2%	MASTERED
Tier 4	Deep Learning Architectures & PyTorch Layers	2,200	25.0%	76.7% (3x 100%)	MASTERED
Tier 5	Applied Machine Learning Breadth & Pipelines	2,160	25.0%	100.0%	MASTERED
Tier 6	Authentic Applied ML & Systems Problem Solving	3,000	25.0%	99.3% (14x 100%, 1x 90%)	MASTERED

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3. Core Competencies & Domain Coverage

Voilum-1 demonstrates reliable zero-shot execution across 30 foundational machine learning pillars:

1. Classical Machine Learning:

   • Principal Component Analysis (PrincipalComponentAnalysis): Mean-centering, sample covariance, eigen-decomposition (np.linalg.eigh), explained variance ratios.
   • Primal Support Vector Machines (LinearSVM_SGD): Stochastic subgradient descent on hinge loss with ( L_2 ) weight regularization.
   • Lloyd's K-Means Clustering (KMeansClustering): Pairwise vectorized Euclidean distance estimation and centroid updates.
   • Gaussian Mixture Model E-Step (gmm_e_step): Posterior responsibility calculation stabilized via Log-Sum-Exp.
   • Ridge Regression (ridge_regression_closed_form): Analytically solving regularized normal equations: $$\beta =(X^{T}X+\lambda I{)}^{-1}{X}^{T}y\backslash beta\; =\; (X^T\; X\; +\; \backslash lambda\; I)^\{-1\}\; X^T\; y$$
   • Vectorized Logistic Regression (logistic_regression_step): Gradient evaluation under binary cross-entropy.
   • Nonparametric ROC-AUC (binary_roc_auc): Wilcoxon-Mann-Whitney rank statistics from scratch.
   • Confusion Matrix Metrics (confusion_matrix_metrics): Exact Accuracy, Precision, Recall, and ( F_1 ).

2. Deep Learning Architectures:

   • Rotary Position Embeddings (apply_rope): 2D complex rotations over paired feature dimensions.
   • Root Mean Square Normalization (RMSNorm): Scale-invariant feature normalization without mean centering (( \epsilon = 10^{-6} )).
   • SwiGLU Gated Feed-Forward (SwiGLUFFN): Gated projection with Swish activation: $$\text{SwiGLU}(x)=(\text{Swish}(x{W}_{\text{gate}})\otimes x{W}_{\text{up}})W_{\text{down}}\backslash text\{SwiGLU\}(x)\; =\; (\backslash text\{Swish\}(x\; W\_\{\backslash text\{gate\}\})\; \backslash otimes\; x\; W\_\{\backslash text\{up\}\})\; W\_\{\backslash text\{down\}\}$$
   • Multi-Head Attention (multi_head_attention): Scaled dot-product attention with causal masking.
   • Grouped-Query Attention (GroupedQueryAttention): Multi-head attention with repeated KV-head broadcasting.
   • Inverted Dropout (InvertedDropout): Training-time activation dropping with ( 1 / (1 - p) ) scaling and eval pass-through.
   • Low-Rank Adaptation (LoRALinear): Parameter-efficient adapters scaling by ( \alpha / r ).
   • Bottleneck Autoencoders (Autoencoder): Symmetrical linear compression and decompression.

3. Loss Functions & Metric Learning:

   • Soft Dice Loss (dice_loss): Continuous spatial overlap loss for segmentation masks.
   • Binary Focal Loss (binary_focal_loss): Dynamically scaled cross-entropy for severe class imbalance.
   • InfoNCE Contrastive Loss (infonce_loss): Temperature-scaled categorical cross-entropy over similarity matrices.
   • Triplet Margin Loss (triplet_margin_loss): Metric learning embedding separation: $$\mathcal{L}(a,p,n)=\max (0,\mathrm{\parallel }f(a)-f(p){\mathrm{\parallel }}_2^2-\mathrm{\parallel }f(a)-f(n){\mathrm{\parallel }}_2^2+m)\backslash mathcal\{L\}(a,\; p,\; n)\; =\; \backslash max\backslash left(0,\; \backslash |f(a)\; -\; f(p)\backslash |\_2^2\; -\; \backslash |f(a)\; -\; f(n)\backslash |\_2^2\; +\; m\backslash right)$$
   • Robust Huber Loss (huber_loss): Piecewise quadratic (( \le \delta )) and linear (( > \delta )) regression loss.
   • Label Smoothing Cross-Entropy (label_smoothing_cross_entropy): Soft target regularization.

4. Systems, Tokenization & Optimization:

   • Cosine Annealing with Warmup (cosine_warmup_lr): Linear ramp followed by half-period cosine decay.
   • Exponential Moving Average (ExponentialMovingAverage): Polyak parameter tracking for inference stabilization.
   • Global Gradient Norm Clipping (clip_grad_norm_): Collective ( L_2 ) gradient rescaling under threshold ( M ).
   • Vector Retrieval (top_k_cosine_similarity): Cosine ranking over dense embedding matrices.
   • Byte Pair Encoding Merge Step (bpe_merge_step): Vocabulary merge operations over token sequences.
   • Machine Translation Evaluation (sentence_bleu): Clipped ( n )-gram precision with brevity penalty.

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4. Real-World Execution Examples (Empirical Model Rollouts)

Below are actual, unedited prompts and corresponding greedy outputs generated by Voilum-1 during evaluation on the NVIDIA DGX Spark cluster. Each solution was validated by the automated unit test compiler sandbox (Reward: 1.0, PASSED).

Example 1: Grouped-Query Attention (Deep Learning Architecture / Attention Mechanisms)

User Prompt:

Write a PyTorch nn.Module class GroupedQueryAttention(nn.Module) with d_model=512, num_heads=8, num_kv_heads=2, head_dim=d_model//num_heads, implementing grouped-query attention where KV heads are repeated to match query heads.

Voilum-1 Generation (Greedy Decoding):

import torch
import torch.nn as nn
import torch.nn.functional as F
import math

class GroupedQueryAttention(nn.Module):
    def __init__(self, d_model: int = 512, num_heads: int = 8, num_kv_heads: int = 2):
        super().__init__()
        self.d_model = d_model
        self.num_heads = num_heads
        self.num_kv_heads = num_kv_heads
        self.head_dim = d_model // num_heads
        self.num_queries_per_kv = num_heads // num_kv_heads
        
        self.q_proj = nn.Linear(d_model, num_heads * self.head_dim, bias=False)
        self.k_proj = nn.Linear(d_model, num_kv_heads * self.head_dim, bias=False)
        self.v_proj = nn.Linear(d_model, num_kv_heads * self.head_dim, bias=False)
        self.out_proj = nn.Linear(d_model, d_model, bias=False)

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        B, T, _ = x.shape
        q = self.q_proj(x).view(B, T, self.num_heads, self.head_dim).transpose(1, 2)
        k = self.k_proj(x).view(B, T, self.num_kv_heads, self.head_dim).transpose(1, 2)
        v = self.v_proj(x).view(B, T, self.num_kv_heads, self.head_dim).transpose(1, 2)
        
        k = k.repeat_interleave(self.num_queries_per_kv, dim=1)
        v = v.repeat_interleave(self.num_queries_per_kv, dim=1)
        
        scale = 1.0 / math.sqrt(self.head_dim)
        attn = (q @ k.transpose(-2, -1)) * scale
        attn = F.softmax(attn, dim=-1)
        out = (attn @ v).transpose(1, 2).contiguous().view(B, T, self.d_model)
        return self.out_proj(out)

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Example 2: Rotary Position Embeddings (Attention & Positional Encodings)

User Prompt:

Write a PyTorch function apply_rope(x: torch.Tensor, cos: torch.Tensor, sin: torch.Tensor) -> torch.Tensor that:

1. Given input x of shape (B, T, H, D) where D is even, and broadcastable frequencies cos, sin (1, T, 1, D).
2. Splits x into two halves: x1 = x[..., :D//2] and x2 = x[..., D//2:].
3. Constructs x_rot = torch.cat((-x2, x1), dim=-1).
4. Returns (x * cos) + (x_rot * sin).

Voilum-1 Generation (Greedy Decoding):

import torch

def apply_rope(x: torch.Tensor, cos: torch.Tensor, sin: torch.Tensor) -> torch.Tensor:
    d = x.shape[-1]
    x1 = x[..., :d // 2]
    x2 = x[..., d // 2:]
    x_rot = torch.cat((-x2, x1), dim=-1)
    return (x * cos) + (x_rot * sin)

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Example 3: Principal Component Analysis (Classical Machine Learning & Dimensionality Reduction)

User Prompt:

Write a Python function pca_project(X: np.ndarray, n_components: int) -> np.ndarray that centers the data matrix X, calculates the sample covariance matrix, performs eigenvalue decomposition, and projects X onto the top n_components principal eigenvectors.

Voilum-1 Generation (Greedy Decoding):

import numpy as np

def pca_project(X: np.ndarray, n_components: int) -> np.ndarray:
    X_centered = X - np.mean(X, axis=0)
    cov = (X_centered.T @ X_centered) / (X.shape[0] - 1)
    eigvals, eigvecs = np.linalg.eigh(cov)
    top_indices = np.argsort(eigvals)[::-1][:n_components]
    top_eigvecs = eigvecs[:, top_indices]
    return X_centered @ top_eigvecs

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Example 4: Root Mean Square Layer Normalization (Deep Learning Architecture)

User Prompt:

Write a PyTorch nn.Module class RMSNorm(nn.Module) with d_model=512 and eps=1e-6 that normalizes inputs using root mean square: x * rsqrt(mean(x^2) + eps) * weight.

Voilum-1 Generation (Greedy Decoding):

import torch
import torch.nn as nn

class RMSNorm(nn.Module):
    def __init__(self, d_model: int = 512, eps: float = 1e-6):
        super().__init__()
        self.eps = eps
        self.weight = nn.Parameter(torch.ones(d_model))

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        variance = x.pow(2).mean(-1, keepdim=True)
        x_norm = x * torch.rsqrt(variance + self.eps)
        return self.weight * x_norm

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Example 5: Primal Support Vector Machine via SGD (Classical Machine Learning)

User Prompt:

Write a binary linear classifier in NumPy: LinearSVM_SGD(lr=0.01, lambda_reg=0.01, epochs=20). It should train a Support Vector Machine using stochastic subgradient descent on the primal hinge loss with L2 regularization for labels in {-1, +1}. Implement fit(X, y) to train the weight vector and bias, and predict(X) to return discrete {-1, +1} class predictions.

Voilum-1 Generation (Greedy Decoding):

import numpy as np

class LinearSVM_SGD:
    def __init__(self, lr: float = 0.01, lambda_reg: float = 0.01, epochs: int = 20):
        self.lr = lr
        self.lambda_reg = lambda_reg
        self.epochs = epochs
        self.w = None
        self.b = 0.0

    def fit(self, X: np.ndarray, y: np.ndarray):
        N, D = X.shape
        self.w = np.zeros(D)
        self.b = 0.0
        for _ in range(self.epochs):
            for i in range(N):
                margin = y[i] * (np.dot(self.w, X[i]) + self.b)
                if margin < 1.0:
                    self.w -= self.lr * (self.lambda_reg * self.w - y[i] * X[i])
                    self.b += self.lr * y[i]
                else:
                    self.w -= self.lr * (self.lambda_reg * self.w)
        return self

    def predict(self, X: np.ndarray) -> np.ndarray:
        return np.where(X @ self.w + self.b >= 0, 1, -1)

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Example 6: Medical Image Segmentation Soft Dice Loss (Loss Functions)

User Prompt:

I'm working on a medical image segmentation pipeline in PyTorch. Can you write a dice_loss(pred, target, smooth=1.0) function? The predictions are predicted probabilities and target is binary mask. It needs to compute the Dice similarity loss between 0 and 1 so that higher overlap gives lower loss, and use the smoothing term to prevent divide-by-zero.

Voilum-1 Generation (Greedy Decoding):

import torch

def dice_loss(pred: torch.Tensor, target: torch.Tensor, smooth: float = 1.0) -> torch.Tensor:
    intersection = (pred * target).sum()
    cardinality = pred.sum() + target.sum()
    dice = (2.0 * intersection + smooth) / (cardinality + smooth)
    return 1.0 - dice

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Example 7: Class-Imbalanced Binary Focal Loss (Loss Functions)

User Prompt:

We have severe class imbalance in our binary classification task where 98% of the samples are negative. Write a PyTorch function binary_focal_loss(pred, target, alpha=0.25, gamma=2.0) that implements focal loss to down-weight the loss contribution from easy well-classified examples.

Voilum-1 Generation (Greedy Decoding):

import torch

def binary_focal_loss(pred: torch.Tensor, target: torch.Tensor, alpha: float = 0.25, gamma: float = 2.0) -> torch.Tensor:
    eps = 1e-12
    p_t = target * pred + (1.0 - target) * (1.0 - pred)
    alpha_t = target * alpha + (1.0 - target) * (1.0 - alpha)
    loss = -alpha_t * ((1.0 - p_t) ** gamma) * torch.log(p_t + eps)
    return loss.mean()

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Example 8: Inverted Dropout with Expectation Preservation (Deep Learning Layers)

User Prompt:

Write an InvertedDropout(p=0.5) module from scratch in PyTorch. During training, randomly drop activations with probability p while scaling active units by 1 / (1 - p) so the expected sum is preserved without needing rescaling during evaluation. In eval mode, it should act as an identity pass-through.

Voilum-1 Generation (Greedy Decoding):

import torch
import torch.nn as nn

class InvertedDropout(nn.Module):
    def __init__(self, p: float = 0.5):
        super().__init__()
        assert 0.0 <= p < 1.0
        self.p = p

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        if not self.training or self.p == 0.0:
            return x
        keep_prob = 1.0 - self.p
        mask = (torch.rand_like(x) < keep_prob).float() / keep_prob
        return x * mask

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Example 9: Byte-Pair Encoding Vocabulary Merge Step (Systems & Tokenization)

User Prompt:

Write a tokenization utility bpe_merge_step(corpus, target_pair, new_token) in Python. Given a corpus of tokenized sentences (lists of token strings), replace all adjacent occurrences of target_pair with new_token throughout the corpus and return the updated corpus.

Voilum-1 Generation (Greedy Decoding):

def bpe_merge_step(corpus: list[list[str]], target_pair: tuple[str, str], new_token: str) -> list[list[str]]:
    p0, p1 = target_pair
    new_corpus = []
    for seq in corpus:
        new_seq = []
        i = 0
        while i < len(seq):
            if i < len(seq) - 1 and seq[i] == p0 and seq[i + 1] == p1:
                new_seq.append(new_token)
                i += 2
            else:
                new_seq.append(seq[i])
                i += 1
        new_corpus.append(new_seq)
    return new_corpus

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5. Quickstart & Usage

5.1 Repository Structure

Voilum-1 is released as a minimal open-weights artifact bundle adhering to industry open-source distribution standards:

elisepaul/voilum-1/
|-- .gitattributes            # Git LFS tracking configuration
|-- README.md                 # Academic model card and technical specifications
|-- config.json               # Architecture metadata and hyperparameter config
|-- generation_config.json    # Default greedy sampling parameters
|-- model.safetensors         # Clean BF16 serialized weights (884.2 MB)
|-- pytorch_model.bin         # Standard PyTorch binary state dict (836.3 MB)
|-- special_tokens_map.json   # ChatML special token delimiters
|-- tokenizer.json            # StarCoder2 BPE vocabulary and merge rules
|-- tokenizer_config.json     # Tokenizer settings and special token mappings
`-- voilum1_nvfp4.pt          # Quantized NVFP4 block-scaled weights (450.2 MB)

5.2 Installation & Requirements

pip install torch transformers safetensors

5.3 Loading Weights

The model weights and tokenizer can be loaded directly from Hugging Face:

from safetensors.torch import load_file
from transformers import AutoTokenizer

# 1. Load Tokenizer
tokenizer = AutoTokenizer.from_pretrained("elisepaul/voilum-1")

# 2. Inspect Architecture Configuration
# config.json contains the exact dimensions (dim=512, n_layers=16, 8 experts, GQA)

# 3. Load SafeTensors Weights
weights = load_file("model.safetensors") # or via hf_hub_download

5.4 ChatML Prompt Format

Voilum-1 was trained and aligned using the standard ChatML template:

<|im_start|>system
You are Voilum, an expert AI assistant specialized in Python, Machine Learning, and Algorithmic Problem Solving.<|im_end|>
<|im_start|>user
Write an RMSNorm(dim, eps=1e-6) module in PyTorch with forward(x: torch.Tensor) -> torch.Tensor.<|im_end|>
<|im_start|>assistant

5.5 Prompting Guide: How to Talk to Voilum-1

Voilum-1 is a 500M Algorithmic Co-Processor, NOT an Open-Ended Conversational Chatbot.
Voilum-1 was aligned under a strict Zero-Thinking / Zero-Boilerplate Policy using GRPO reinforcement learning. It does not output conversational pleasantries ("Sure, I can help with that!"), markdown chatter, or chain-of-thought monologue. Instead, it is reinforced to immediately emit compilable, assertion-passing Python code starting directly with imports or function definitions.

The "Ignition Formula"

To unlock Voilum-1's peak mathematical accuracy (99.3% greedy pass rate), frame prompts as direct functional specifications with explicit signatures and libraries:

Write a [function / module] <name>(<args>) in [NumPy / PyTorch] that [mathematical objective].

❌ Ineffective Prompts (Casual / Conversational)	Effective Prompts (Interface Specification)
"Hey, how do I write ridge regression?"	Write a function ridge_regression_closed_form(X, y, alpha=1.0) in NumPy that computes the analytical closed-form solution for ridge regression using the normal equations.
"Can you help me compute GMM responsibilities?"	Write a function gmm_e_step(X, pi, mu, sigma) in NumPy that computes posterior responsibilities using log-sum-exp.
"I need a custom normalization layer for my model."	Write a PyTorch nn.Module class RMSNorm(nn.Module) with d_model=512 and eps=1e-6 that normalizes inputs using root mean square.
"Explain how to calculate Dice loss for masks."	Write a PyTorch function dice_loss(pred, target, smooth=1.0) that computes the soft Dice loss between predicted probabilities and binary masks.

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5.6 Curated Prompts to Try (Verified Mastered Tasks)

Below is a curated set of verified benchmark prompts across different domains that you can copy and paste directly into the model:

Domain	Ready-to-Run Prompt	Expected Output / Architecture
Classical ML	Write a function ridge_regression_closed_form(X, y, alpha=1.0) in NumPy that computes the analytical closed-form solution for ridge regression (L2 regularized linear regression) using the normal equations.	Closed-form normal equations: np.linalg.solve(X.T @ X + reg, X.T @ y)
Dimensionality Reduction	Write a Python function pca_project(X: np.ndarray, n_components: int) -> np.ndarray that centers data matrix X, calculates the sample covariance matrix, performs eigenvalue decomposition, and projects X onto the top n_components principal eigenvectors.	Covariance centering, np.linalg.eigh, and projection
Transformer Architectures	Write a PyTorch nn.Module class GroupedQueryAttention(nn.Module) with d_model=512, num_heads=8, num_kv_heads=2, head_dim=d_model//num_heads, implementing grouped-query attention where KV heads are repeated to match query heads.	GQA with repeat_interleave, scaled dot-product attention
Positional Encodings	Write a PyTorch function apply_rope(x: torch.Tensor, cos: torch.Tensor, sin: torch.Tensor) -> torch.Tensor that rotates input x of shape (B, T, H, D) using broadcastable rotary frequencies cos and sin.	Complex 2D rotary coordinate rotation
Layer Normalization	Write a PyTorch nn.Module class RMSNorm(nn.Module) with d_model=512 and eps=1e-6 that normalizes inputs using root mean square: x * rsqrt(mean(x^2) + eps) * weight.	Root-mean-square normalization with learnable gain
Optimization & Classifiers	Write a binary linear classifier in NumPy: LinearSVM_SGD(lr=0.01, lambda_reg=0.01, epochs=20). Implement fit(X, y) using stochastic subgradient descent on primal hinge loss with L2 regularization, and predict(X) returning {-1, +1}.	Primal SGD hinge loss subgradient descent
Medical / Vision Losses	Write a PyTorch function dice_loss(pred, target, smooth=1.0) where pred are predicted probabilities and target is binary mask. Compute Dice similarity loss between 0 and 1 with smoothing.	Intersection-over-cardinality soft Dice loss
Regularization Layers	Write an InvertedDropout(p=0.5) module from scratch in PyTorch. During training, drop activations with probability p while scaling active units by 1/(1-p). In eval mode, act as identity.	Expectation-preserving inverted dropout
Tokenization Systems	Write a tokenization utility bpe_merge_step(corpus, target_pair, new_token) in Python. Given a corpus of tokenized sentences, replace all adjacent occurrences of target_pair with new_token throughout the corpus.	Pure Python sliding-window BPE pair replacement

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6. Hardware Efficiency & Empirical Inference Benchmarks

All inference performance metrics below were empirically measured and verified on physical hardware:

6.1 Target Hardware & Environment

• Platform: NVIDIA DGX Spark (Unified Memory Architecture)
• GPU Accelerator: NVIDIA GB10 Blackwell GPU
• Precision Format: bfloat16 (model.safetensors)
• Operating Power Envelope: ~15W - 25W sustained draw

6.2 Measured Empirical Benchmark Comparison: BF16 vs. Blackwell NVFP4

Measured on the NVIDIA DGX Spark (NVIDIA GB10 Blackwell GPU) with warm-up passes and exact CUDA event synchronization over consecutive 128-token generation trials:

Metric	BF16 SafeTensors (model.safetensors)	Blackwell NVFP4 (voilum1_nvfp4.pt)	Measurement / Impact
Quantization Format	Uncompressed BF16	NVFP4 (( E2M1 ) Micro-scaled, Block Size 16)	Native Blackwell block-scaling
Serialized Disk Footprint	884.2 MB	450.2 MB	~2x on-disk weight compaction
Generation Speed	57.6 tokens / sec	58.2 tokens / sec	Empirically verified across multiple trials
Per-Token Latency	17.4 ms / token	17.2 ms / token	Mean token-to-token autoregressive latency
Peak Active VRAM	946.2 MiB	1,830.3 MiB	Active inference memory envelope

6.3 Standardized llama-benchy Evaluation Matrix

Benchmark executed on the NVIDIA DGX Spark GB10 GPU using llama-benchy (3 runs per configuration, Project Gutenberg natural text corpus, API latency mode):

Model	Benchmark Evaluation	Throughput (tok/s)	Peak (tok/s)	TTFR (ms)	Est. PPT (ms)	E2E TTFT (ms)
voilum-1	pp128 (Prompt Processing)	5,391.91 +/- 192.90	--	21.54 +/- 0.70	19.87 +/- 0.70	21.54 +/- 0.70
voilum-1	tg32 (Token Generation)	57.67 +/- 0.29	59.53 +/- 0.30	--	--	--
voilum-1	pp128 (Prompt Processing)	5,066.83 +/- 219.48	--	22.83 +/- 0.91	21.16 +/- 0.91	22.83 +/- 0.91
voilum-1	tg64 (Token Generation)	56.65 +/- 0.50	57.00 +/- 0.82	--	--	--
voilum-1	pp512 (Prompt Processing)	19,541.66 +/- 2,003.38	--	27.09 +/- 2.80	25.41 +/- 2.80	27.09 +/- 2.80
voilum-1	tg32 (Token Generation)	51.53 +/- 0.87	53.19 +/- 0.90	--	--	--
voilum-1	pp512 (Prompt Processing)	21,276.51 +/- 158.03	--	24.75 +/- 0.17	23.08 +/- 0.17	24.75 +/- 0.17
voilum-1	tg64 (Token Generation)	52.19 +/- 0.63	52.67 +/- 0.94	--	--	--

6.4 Multi-Client High-Concurrency Throughput Scaling (llama-benchy)

Evaluated on the NVIDIA DGX Spark GB10 Blackwell GPU using llama-benchy across scaling concurrency levels up to 200 parallel streams (pp128, tg32, 2 runs per configuration, Project Gutenberg natural text corpus):

Concurrency Level	Stage / Metric	Total Aggregate Throughput (t/s total)	Per-Request Throughput (t/s req)	Peak Aggregate Throughput (peak t/s)	End-to-End TTFT (e2e_ttft)
( C = 1 )	Prompt Processing (pp128) Token Generation (tg32)	5,561.51 +/- 66.48 tok/s 55.53 +/- 0.45 tok/s	5,561.51 +/- 66.48 tok/s 55.53 +/- 0.45 tok/s	-- 57.32 +/- 0.46 tok/s	21.25 +/- 0.23 ms --
( C = 16 )	Prompt Processing (pp128) Token Generation (tg32)	24,629.06 +/- 2,505.44 tok/s 532.38 +/- 9.98 tok/s	2,426.98 +/- 1,001.51 tok/s 34.65 +/- 0.46 tok/s	-- 549.63 +/- 10.30 tok/s	54.00 +/- 19.68 ms --
( C = 64 )	Prompt Processing (pp128) Token Generation (tg32)	45,503.99 +/- 14,026.36 tok/s 776.14 +/- 11.45 tok/s	1,001.12 +/- 428.98 tok/s 12.65 +/- 1.02 tok/s	-- 826.50 +/- 5.50 tok/s	119.90 +/- 31.18 ms --
( C = 128 )	Prompt Processing (pp128) Token Generation (tg32)	46,867.24 +/- 15,447.84 tok/s 761.18 +/- 2.72 tok/s	602.60 +/- 337.15 tok/s 6.18 +/- 0.06 tok/s	-- 886.00 +/- 4.00 tok/s	211.41 +/- 69.87 ms --
( C = 200 )	Prompt Processing (pp128) Token Generation (tg32)	50,090.83 +/- 18,442.76 tok/s 617.22 +/- 107.46 tok/s	384.67 +/- 182.53 tok/s 3.19 +/- 0.56 tok/s	-- 700.00 +/- 100.00 tok/s	315.04 +/- 114.08 ms --

Key Findings:

• Prefill Scaling: Batch prefill processing scales from 5,561 tokens/sec at ( C=1 ) to 50,090+ tokens/sec under 200 concurrent requests.
• Aggregate Generation Throughput: Continuous dynamic batching achieves a ~14x aggregate speedup, scaling from 55.5 tokens/sec at single concurrency to an aggregate peak of 886.00 tokens/sec at ( C=128 ) and 700.00 tokens/sec at ( C=200 ).

Empirical Integrity Note: Only directly measured on-device numbers are reported. Theoretical extrapolations and unverified hardware estimates are omitted.

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7. Limitations & Intended Use

7.1 Intended Use Cases

Voilum-1 is an execution-grounded Small Language Model (SLM) engineered specifically for:

• Algorithmic Co-Processing: Real-time generation of verified mathematical subroutines, tensor transformations, and numerical algorithms.
• Deep Learning Systems Development: Synthesis of PyTorch modules (custom attention mechanisms, normalization layers, loss functions, optimizers).
• Scientific & Applied ML Workflows: Numerical computing pipelines utilizing NumPy, SciPy, and Scikit-Learn.
• Edge & High-Throughput Deployment: Low-latency edge execution on NVIDIA hardware utilizing minimal memory footprints (<1 GB BF16, ~450 MB NVFP4).

7.2 Explicit Architectural Limitations

1. Sub-1B Parameter Manifold (Laser vs. Floodlight)
   At 463.6M parameters (100.8M active), Voilum-1 represents a high-density specialized computational engine rather than a multi-billion-parameter generalist. It has razor-sharp representations for algorithmic and mathematical structures, but its attention activations are tightly conditioned on structured problem prompts. Vague, conversational, or ambiguous queries will lead to low-confidence outputs.

2. Zero-Boilerplate Policy (Not a Conversational Chatbot)
   Voilum-1 was trained with a Zero-Thinking / Zero-Boilerplate policy under GRPO reinforcement learning. It does not engage in conversational small talk, casual dialogue, or open-ended chit-chat. It will not output introductory remarks ("Hello! I would be delighted to help you write...") or conversational sign-offs.

3. Single-Turn Functional Synthesis
   The model is optimized for single-turn code generation given explicit functional specifications. It is not designed for multi-turn conversational memory, role-playing, or extensive back-and-forth dialogue across long conversation threads.

4. Domain Boundaries
   Voilum-1 is strictly focused on Python (scientific, algorithmic, and deep learning). It is not evaluated or intended for:

   • Non-Python programming languages (C++, Rust, JavaScript, HTML/CSS).
   • Creative writing, fiction, poetry, or general conversational Q&A.
   • Open-domain world trivia, historical facts, or legal/medical advice.
   • Execution of untrusted code without an external isolated sandbox.

5. Prompt Formatting Sensitivity
   Because the model was aligned with ChatML delimiters (<|im_start|> / <|im_end|>), optimal adherence requires preserving the ChatML format. Raw unformatted text completions may result in sub-optimal token routing across the MoE gating network.

---

8. References & Foundational Literature

The architecture, training curriculum, and alignment methodology of Voilum-1 build upon the following foundational research:

1. Root Mean Square Layer Normalization (RMSNorm)
   Biao Zhang, Rico Sennrich. Advances in Neural Information Processing Systems (NeurIPS 2019), 32, 2019.
   [arXiv:1910.07467]

2. GQA: Training Generalized Multi-Query Transformer Models from Multi-Head Checkpoints
   Joshua Ainslie, James Lee-Thorp, Michiel de Jong, Yury Zemlyanskiy, Federico Lebrón, Sumit Sanghai. EMNLP, 2023.
   [arXiv:2305.13245]

3. RoFormer: Enhanced Transformer with Rotary Position Embedding (RoPE)
   Jianlin Su, Murtadha Ahmed, Yu Lu, Shengfeng Pan, Wen Bo, Yunfeng Liu. Neurocomputing, 568:127063, 2024.
   [arXiv:2104.09864]

4. GLU Variants Improve Transformer (SwiGLU)
   Noam Shazeer. arXiv preprint arXiv:2002.05202, 2020.
   [arXiv:2002.05202]

5. Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer
   Noam Shazeer, Azalia Mirhoseini, Krzysztof Maziarz, Andy Davis, Quoc Le, Geoffrey Hinton, Jeff Dean. International Conference on Learning Representations (ICLR), 2017.
   [arXiv:1701.06538]

6. FlashAttention-2: Faster Attention with Better Parallelism and Work Partitioning
   Tri Dao. International Conference on Learning Representations (ICLR), 2024.
   [arXiv:2307.08691]

7. Microscaling Formats for Deep Learning: OCP MX Specification (NVFP4)
   Bita Darvish Rouhani et al. arXiv preprint arXiv:2310.10537, 2023.
   [arXiv:2310.10537]

8. DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models (GRPO)
   Zhihong Shao, Peiyi Wang, Qihao Zhu, Runxin Xu, Junxiao Song, Mingchuan Zhang, Y.K. Zhang, Y. Wu, Daya Guo. arXiv preprint arXiv:2402.03300, 2024.
   [arXiv:2402.03300]

9. Training Language Models to Follow Instructions with Human Feedback (InstructGPT)
   Long Ouyang, Jeffrey Wu, Xu Jiang, Diogo Almeida, Carroll Wainwright, Pamela Mishkin, Chong Zhang, Sandhini Agarwal, Katarina Slama, Alex Ray, et al. Advances in Neural Information Processing Systems (NeurIPS 2022), 35:27730–27744, 2022.
   [arXiv:2203.02155]

10. StarCoder 2 and The Stack v2: The Next Generation
    Anton Lozhkov, Raymond Li, Loubna Ben Allal, Federico Cassano, Joel Lamy-Poirier, Nouamane Tazi, Ao Tang, Sampo Pyysalo, Nicole Liu, Yuxiang Zi, et al. arXiv preprint arXiv:2402.19173, 2024.
    [arXiv:2402.19173]

Click to expand raw BibTeX entries

@article{zhang2019rmsnorm,
  title={Root Mean Square Layer Normalization},
  author={Zhang, Biao and Sennrich, Rico},
  journal={Advances in Neural Information Processing Systems (NeurIPS)},
  volume={32},
  year={2019},
  url={https://arxiv.org/abs/1910.07467}
}

@article{ainslie2023gqa,
  title={GQA: Training Generalized Multi-Query Transformer Models from Multi-Head Checkpoints},
  author={Ainslie, Joshua and Lee-Thorp, James and de Jong, Michiel and Zemlyanskiy, Yury and Lebr{\'o}n, Federico and Sanghai, Sumit},
  journal={EMNLP},
  year={2023},
  url={https://arxiv.org/abs/2305.13245}
}

@article{su2024roformer,
  title={RoFormer: Enhanced Transformer with Rotary Position Embedding},
  author={Su, Jianlin and Ahmed, Murtadha and Lu, Yu and Pan, Shengfeng and Bo, Wen and Liu, Yunfeng},
  journal={Neurocomputing},
  volume={568},
  pages={127063},
  year={2024},
  url={https://arxiv.org/abs/2104.09864}
}

@article{shazeer2020glu,
  title={GLU Variants Improve Transformer},
  author={Shazeer, Noam},
  journal={arXiv preprint arXiv:2002.05202},
  year={2020},
  url={https://arxiv.org/abs/2002.05202}
}

@inproceedings{shazeer2017moe,
  title={Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer},
  author={Shazeer, Noam and Mirhoseini, Azalia and Maziarz, Krzysztof and Davis, Andy and Le, Quoc and Hinton, Geoffrey and Dean, Jeff},
  booktitle={International Conference on Learning Representations (ICLR)},
  year={2017},
  url={https://arxiv.org/abs/1701.06538}
}

@article{dao2023flashattention2,
  title={FlashAttention-2: Faster Attention with Better Parallelism and Work Partitioning},
  author={Dao, Tri},
  journal={International Conference on Learning Representations (ICLR)},
  year={2024},
  url={https://arxiv.org/abs/2307.08691}
}

@article{rouhani2023microscaling,
  title={Microscaling Formats for Deep Learning: OCP MX Specification},
  author={Rouhani, Bita Darvish and others},
  journal={arXiv preprint arXiv:2310.10537},
  year={2023},
  url={https://arxiv.org/abs/2310.10537}
}

@article{shao2024deepseekmath,
  title={DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models},
  author={Shao, Zhihong and Wang, Peiyi and Zhu, Qihao and Xu, Runxin and Song, Junxiao and Zhang, Mingchuan and Zhang, YK and Wu, Y and Guo, Daya},
  journal={arXiv preprint arXiv:2402.03300},
  year={2024},
  url={https://arxiv.org/abs/2402.03300}
}

@article{ouyang2022training,
  title={Training language models to follow instructions with human feedback},
  author={Ouyang, Long and Wu, Jeffrey and Jiang, Xu and Almeida, Diogo and Wainwright, Carroll and Mishkin, Pamela and Zhang, Chong and Agarwal, Sandhini and Slama, Katarina and Ray, Alex and others},
  journal={Advances in Neural Information Processing Systems (NeurIPS)},
  volume={35},
  pages={27730--27744},
  year={2022},
  url={https://arxiv.org/abs/2203.02155}
}

@article{lozhkov2024starcoder2,
  title={StarCoder 2 and The Stack v2: The Next Generation},
  author={Lozhkov, Anton and Li, Raymond and Allal, Loubna Ben and Cassano, Federico and Lamy-Poirier, Joel and Tazi, Nouamane and Tang, Ao and Pyysalo, Sampo and Liu, Nicole and Zi, Yuxiang and others},
  journal={arXiv preprint arXiv:2402.19173},
  year={2024},
  url={https://arxiv.org/abs/2402.19173}
}

---

9. Authorship & Development

• Lead Researcher & Developer: Elise Paul (@elisepaul)
• License: Apache 2.0

---

10. Acknowledgements & AI Assistance Disclosure

This project was developed with the assistance of agentic AI coding assistants (Google DeepMind Antigravity) for automated task scripting, hyperparameter verification, and code refactoring. All experimental design, domain dataset curation, model architecture synthesis, NVIDIA DGX Spark cluster execution, and verification of mathematical proofs were directed and validated by the lead author.

---

11. Citation

If you utilize Voilum-1 in your academic research or applications, please cite:

@misc{paul2026voilum1,
  author = {Paul, Elise},
  title = {Voilum-1: An Execution-Grounded Mixture-of-Experts SLM for Computational Python and Machine Learning Systems},
  year = {2026},
  publisher = {Hugging Face},
  howpublished = {\url{https://huggingface.co/elisepaul/voilum-1}}
}

---

12. License

Voilum-1 is licensed under the Apache 2.0 License.